The measure of one interior angle of a parallelogram is 30 degrees less than 9 times the measure of another angle. Find the measure of each angle.

Answers

Answer 1

Answer:

The interior angles of the parallelogram are either:

XXX

{

159

,

21

,

159

,

21

}

or

XXX

{

3

3

4

,

176

1

4

,

3

1

4

,

176

1

4

}

Explanation:

Case 1: The given relation applies to consecutive angles

Consecutive angles of a parallelogram add up to  

180

Let  

a

and  

b

be consecutive angles (measured in degrees) such that the given relation holds:

XXX

a

=

9

b

30

and since  

a

+

b

=

180

b

=

180

a

XXX

a

=

9

(

180

a

)

30

=

1620

9

a

30

=

1590

9

a

XXX

10

a

=

1590

XXX

a

=

159

and

XXX

b

=

180

a

=

21

Case 2: The given relation applies to opposite angles

Opposite angles of a parallelogram are equal.

Let  

a

be the measure (in degrees) of the referenced opposite angles (and  

b

be the measure of the other two angles:  

a

+

b

=

180

)

We are told

XXX

a

=

9

a

30

Therefore

XXX

8

a

=

30

XXX

a

=

3

3

4

XXX

b

=

180

a

=

176

1

4

Answer link

EZ as pi

Sep 25, 2016

The angles are  

21

°

,

159

°

,

21

°

,

159

°

Explanation:

In a parallelogram, there are only two sizes of angle - two are acute and two are obtuse.

Opposite angles are equal .

Consecutive angles are supplementary because they are co-interior angle on parallel lines.

An additional solution to the one given by Alan P is using the fact that the sum of the interior angles of a parallelogram is 360°.

Let one angle be  

x

The size of the other angle is given by  

9

x

30

2

x

+

2

(

9

x

30

)

=

360

   

sum of the angles is 360°

2

x

+

18

x

60

=

360

20

x

=

420

x

=

21

°

The obtuse angles are each  

180

21

=

159

°

The other option where the given angle is the opposite angle is described is well explained by Alan P.

Step-by-step explanation:

Answer 2

The interior angles of the parallelogram are 21° and 159° respectively.

What is parallelogram?

A parallelogram is defined as a quadrilateral in which both pairs of opposite sides are parallel and equal.

In a parallelogram opposite interior angles are equal and the angles on the same side of the traversal are supplementary (i.e) 180°

For the given situation,

The measure of one interior angle be [tex]x[/tex] and

Another angle was given as [tex]9x-30[/tex]°  

⇒[tex]x+9x-30[/tex]°[tex]=180[/tex]°

⇒[tex]10x=180[/tex]°[tex]+30[/tex]°

⇒[tex]10x=210[/tex]°

On dividing [tex]10[/tex] on both sides,

⇒[tex]\frac{10x}{10}=\frac{210}{10}[/tex]

⇒[tex]x=21[/tex]°

So, another angle is [tex]9x-30[/tex] = [tex]9[/tex]×[tex]21-30[/tex]

⇒[tex]189-30[/tex]

⇒[tex]159[/tex]°

Hence we can conclude that the interior angles of the parallelogram are 21° and 159°.

Learn more about the interior angle of parallelogram here

https://brainly.com/question/8615842

#SPJ2


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Answers

Answer:

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Answer:

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Answers

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Step-by-step explanation:

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Answers

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Answers

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Step-by-step explanation:

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Answers

Answer:

B. 22

Step-by-step explanation:

3 * 5 + 5 * 3 = (2 * 3 - 3 * 5 + 3 * 5) + ( 2 * 5 - 3 * 3 + 5 * 3)

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

Given :

the number has three digits

it is multiple of 20

hundreds digit and tens digit add to make 9

half of it is less than 100.

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Answers

Answer:

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Answers

Thank you very much and this “question” was very helpful for me.

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer

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Answers

Answer:

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Step-by-step explanation:

Answer:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Answers

Answer:

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Step-by-step explanation:

Please find the complete question in the attached file.

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:
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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Help!!
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Answers

Answer:

XZ = 2.5 BD

Step-by-step explanation:

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[tex]\frac{6}{8}[/tex] = [tex]\frac{XZ}{20}[/tex]

⇒ XZ = [tex]\frac{20*6}{8}[/tex]

         = 15

XZ = 15

So that,

BD:XZ = 6:15

           = 1:2.5

Therefore, the relationship between BD and XZ is XZ = 2.5 BD.

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Answers

Answer:

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

the equation will be  2(6x+10+4x+1)

simplified to

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simplified to

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Thank you, Hope it helps

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